Explanations of the genuine openness of the future often appeal to objective indeterminacy. According to the received view, such indeterminacy is indeterminacy of certain future-tensed state of affairs that presently obtain. We shall call this view the weak indeterminate present, to distinguish it from the view we will defend in this paper, which we dub the strong indeterminate present. According to our view, unsettledness of the future is grounded on the present indeterminacy of some present-tensed state of affairs. In order (...) for an indeterminate present-tensed state of affairs to explain the unsettledness of a future-tensed state of affairs, there has to be a connection between the two. We argue that this connection can only be provided if we look at the internal structure of the relevant state of affairs. Finally, we will suggest that the best background theory to explain the connection are the so-called spontaneous collapse models of quantum mechanics. (shrink)

In this chapter, I will discuss what it takes for a dynamical collapse theory to provide a reasonable description of the actual world. I will start with discussions of what is required, in general, of the ontology of a physical theory, and then apply it to the quantum case. One issue of interest is whether a collapse theory can be a quantum state monist theory, adding nothing to the quantum state and changing only its dynamics. Although this was one of (...) the motivations for advancing such theories, its viability has been questioned, and it has been argued that, in order to provide an account of the world, a collapse theory must supplement the quantum state with additional ontology, making such theories more like hidden-variables theories than would first appear. I will make a case for quantum state monism as an adequate ontology, and, indeed, the only sensible ontology for collapse theories. This will involve taking dynamical variables to possess, not sharp values, as in classical physics, but distributions of values. (shrink)

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (QFT) (that is, the ‘naive’ (QFT) used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian (QFT) has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least (...) as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work. (shrink)

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single (...) case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss (...) the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory. (shrink)

Although many physicists have little interest in philosophical arguments about their subject, an analysis of debates about the paradoxes of quantum mechanics shows that their disagreements often depend upon assumptions about the relationship between theories and the real world. Some consider that physics is about building mathematical models which necessarily have limited domains of applicability, while others are searching for a final theory of everything, to which their favourite theory is supposed to be an approximation. We discuss some particular recent (...) debates about quantum theory in which the underlying assumptions are not fully articulated. Introduction Setting the scene The Ghirardi, Rimini and Weber theory Quantum marbles Radioactive decay and isomerism The limits of quantum theory. (shrink)

This book discusses fundamental topics on contemporary Ockhamism. The collected essays show how contemporary Ockhamism can impact areas of research such as semantics, metaphysics and also the philosophy of science. In addition, the volume hosts one historian of Medieval philosophy who investigates the way in which William of Ockham “in flesh and bone” construed time and, more generally, future contingency. The essays explore the different meanings of this theory. They cover three main topics, in particular. The first examines the thesis (...) that sentences and propositions about the future have a definite truth value, without any ensuing commitment to determinism or fatalism. The second topic looks at the problem whether the branching-time model needs to countenance a privileged branch (the so-called Thin Red Line). Finally, the third topic considers the idea that there are so-called soft facts. These would be the subject matter of sentences and propositions verbally about the present or the past, but metaphysically about a later time, and which might change in the future. Overall, the book provides an updated and rigorous idea of the debate about Ockhamism. It gives readers a deeper understanding into this philosophical approach influenced by William of Ockham, characterized by the rejection of the Aristotelian idea that, in order to preserve the contingency of the future, future contingents must be deemed neither true nor false. (shrink)

Quantum mechanics, with its revolutionary implications, has posed innumerable problems to philosophers of science. In particular, it has suggested reconsidering basic concepts such as the existence of a world that is, at least to some extent, independent of the observer, the possibility of getting reliable and objective knowledge about it, and the possibility of taking (under appropriate circumstances) certain properties to be objectively possessed by physical systems. It has also raised many others questions which are well known to those involved (...) in the debate on the interpretation of this pillar of modern science. One can argue that most of the problems are not only due to the intrinsic revolutionary nature of the phenomena which have led to the development of the theory. They are also related to the fact that, in its standard formulation and interpretation, quantum mechanics is a theory which is excellent (in fact it has met with a success unprecedented in the history of science) in telling us everything about what we observe, but it meets with serious difficulties in telling us what is. We are making here specific reference to the central problem of the theory, usually referred to as the measurement problem, or, with a more appropriate term, as the macro-objectification problem. It is just one of the many attempts to overcome the difficulties posed by this problem that has led to the development of Collapse Theories, i.e., to the Dynamical Reduction Program (DRP). As we shall see, this approach consists in accepting that the dynamical equation of the standard theory should be modified by the addition of stochastic and nonlinear terms. The nice fact is that the resulting theory is capable, on the basis of a unique dynamics which is assumed to govern all natural processes, to account at the same time for all well-established.. (shrink)

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics.In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to (...) modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation of the problem. (shrink)

Spontaneous collapse theories of quantum mechanics require an interpretation if their claim to solve the measurement problem is to be vindicated. The most straightforward interpretation rule, the fuzzy link, generates a violation of common sense known as the counting anomaly. Recently, a consensus has developed that the mass density link provides an appropriate interpretation of spontaneous collapse theories that avoids the counting anomaly. In this paper, I argue that the mass density link violates common sense in just as striking a (...) way as the fuzzy link, and hence should not be regarded as a problem-free alternative to the fuzzy link. Hence advocates of spontaneous collapse theories must accept some violation of common sense, although this is not necessarily fatal to their project. (shrink)

This article provides an overview of the philosophical literature on the GRW theory of quantum mechanics, and argues for a particular position regarding that literature. Much of the literature is ontological; it attempts to defend a conception of what the world is like according to the GRW theory against perceived competitors. I argue that there is no real debate here, since these supposedly conflicting positions are better regarded as alternative and compatible ways of describing the world of the GRW theory.

We analyse a recent paper in which an alleged devastating criticism of the so called GRW proposal to account for the objectification of the properties of macroscopic systems has been presented and we show that the author has not taken into account the precise implications of the GRW theory. This fact makes his conclusions basically wrong. We also perform a survey of measurement theory aimed to focus better on the physical and the conceptual aspects of the so-called macro-objectification problem.

The aim of this article is twofold. Recently, Lewis has presented an argument, now known as the "counting anomaly", that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof of the fact that (...) the composition principle, which holds true in standard quantum mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of such interpretations. Once this flaw is uncovered, the anomaly vanishes. (shrink)

The paper argues that the formulation of quantum mechanics proposed by Ghirardi, Rimini and Weber (GRW) is a serious candidate for being a fundamental physical theory and explores its ontological commitments from this perspective. In particular, we propose to conceive of spatial superpositions of non-massless microsystems as dispositions or powers, more precisely propensities, to generate spontaneous localizations. We set out five reasons for this view, namely that (1) it provides for a clear sense in which quantum systems in entangled states (...) possess properties even in the absence of definite values; (2) it vindicates objective, single-case probabilities; (3) it yields a clear transition from quantum to classical properties; (4) it enables to draw a clear distinction between purely mathematical and physical structures, and (5) it grounds the arrow of time in the time-irreversible manifestation of the propensities to localize. (shrink)

The paper makes a case for there being causation in the form of causal properties or causal structures in the domain of fundamental physics. That case is built in the first place on an interpretation of quantum theory in terms of state reductions so that there really are both entangled states and classical properties, GRW being the most elaborate physical proposal for such an interpretation. I then argue that the interpretation that goes back to Everett can also be read in (...) a causal manner, the splitting of the world being conceivable as a causal process. Finally, I mention that the way in which general relativity theory conceives the metrical field opens up the way for a causal conception of the metrical properties as well. (shrink)

A few years ago, I argued that according to spontaneous collapse theories of quantum mechanics, arithmetic applies to macroscopic objects only as an approximation. Several authors have written articles defending spontaneous collapse theories against this charge, including Bassi and Ghirardi, Clifton and Monton, and now Frigg. The arguments of these authors are all different and all ingenious, but in the end I think that none of them succeeds, for reasons I elaborate here. I suggest a fourth line of response, based (...) on an analogy with epistemic paradoxes, which I think is the best way to defend spontaneous collapse theories, and which leaves my main thesis intact. (shrink)

Lewis 313) has recently presented an argument claiming that, under the Ghirardi–Rimini–Weber theory of quantum mechanics, arithmetic does not apply to ordinary macroscopic objects such as marbles . In this paper, I disentangle two different lines of Lewis's argument, one devoted to what I call the standard GRW interpretation and the other to the mass density interpretation . I present both strains of Lewis's argument, and move on to criticise Lewis's position, focusing on his argument with respect to MDI. I (...) analyse the structure of his argument, and follow this with a novel refutation of Lewis's argument, drawing on the original presentation of MDI as developed by Ghirardi et al. 5). I briefly consider the debate that ensued between Bassi and Ghirardi and Clifton and Monton and interpret it within the context of my analysis. I conclude that Lewis's Counting Anomaly fails to generate a genuine problem. (shrink)

Constructive empiricism - as formulated by Bas van Fraassen - makes no epistemological claims about the nature of science. Rather, it is a view about the aim of science, to be situated within van Fraassen's broader voluntarist epistemology. Yet while this epistemically minimalist framework may have various advantages in defending the epistemic relevance of constructive empiricism, I show how it also has various disadvantages in maintaining its internal coherence.

It seems to be widely assumed that the only effect of the Ghirardi-Rimini-Weber dynamical collapse mechanism on the `tails' of the wavefunction is to reduce their weight. In consequence it seems to be generally accepted that the tails behave exactly as do the various branches in the Everett interpretation except for their much lower weight. These assumptions are demonstrably inaccurate: the collapse mechanism has substantial and detectable effects within the tails. The relevance of this misconception for the dynamical-collapse theories is (...) debatable, though. (shrink)

Spontaneous collapse theories of quantum mechanics require an interpretation if their claim to solve the measurement problem is to be vindicated. The most straightforward interpretation rule, the fuzzy link, generates a violation of common sense known as the counting anomaly. Recently, a consensus has developed that the mass density link provides an appropriate interpretation of spontaneous collapse theories that avoids the counting anomaly. In this paper, I argue that the mass density link violates common sense in just as striking a (...) way as the fuzzy link, and hence should not be regarded as a problem-free alternative to the fuzzy link. Hence advocates of spontaneous collapse theories must accept some violation of common sense, although this is not necessarily fatal to their project. (shrink)

The question of how to interpret spontaneous collapse theories of quantum mechanics is an open one. One issue involves what link one should use to go from wave function talk to talk of ordinary macroscopic objects. Another issue involves whether that link should be taken ontologically seriously. In this paper, I ague that the link should be taken ontologically seriously; I argue against an ontology consisting solely of the wave function. I then consider three possible links: the fuzzy link, the (...) accessible mass density link, and the mass density simpliciter link. I show that the first two links have serious anomalies which render them unacceptable. I show that the mass density simpliciter link, in contrast, is viable. (shrink)

In my dissertation I analyze the structure of fundamental physical theories. I start with an analysis of what an adequate primitive ontology is, discussing the measurement problem in quantum mechanics and theirs solutions. It is commonly said that these theories have little in common. I argue instead that the moral of the measurement problem is that the wave function cannot represent physical objects and a common structure between these solutions can be recognized: each of them is about a clear three-dimensional (...) primitive ontology that evolves according to a law determined by the wave function. The primitive ontology is what matter is made of while the wave function tells the matter how to move. One might think that what is important in the notion of primitive ontology is their three-dimensionality. If so, in a theory like classical electrodynamics electromagnetic fields would be part of the primitive ontology. I argue that, reflecting on what the purpose of a fundamental physical theory is, namely to explain the behavior of objects in three--dimensional space, one can recognize that a fundamental physical theory has a particular architecture. If so, electromagnetic fields play a different role in the theory than the particles and therefore should be considered, like the wave function, as part of the law. Therefore, we can characterize the general structure of a fundamental physical theory as a mathematical structure grounded on a primitive ontology. I explore this idea to better understand theories like classical mechanics and relativity, emphasizing that primitive ontology is crucial in the process of building new theories, being fundamental in identifying the symmetries. Finally, I analyze what it means to explain the word around us in terms of the notion of primitive ontology in the case of regularities of statistical character. Here is where the notion of typicality comes into play: we have explained a phenomenon if the typical histories of the primitive ontology give rise to the statistical regularities we observe. (shrink)

In view of the arguments put forward by Clifton and Monton [this volume], we reconsider the alleged conflict of dynamical reduction models with the enumeration principle. We prove that our original analysis of such a problem is correct, that the GRW model does not meet any difficulty and that the reasoning of the above authors is inappropriate since it does not take into account the correct interpretation of the dynamical reduction theories.

The very formal structure of quantum mechanics implies the loss of individuality of physical systems and it requires to look at the Universe as an unbroken whole. The main reason for which, within such a theory, one must renounce to a clear identification of the parts and the whole is the superposition principle which stays at the basis of the theory. It implies, as well known, the phenomenon of entanglement which, in the most extreme case, entails that the constituents of (...) a composite system do not possess any objective property; only the system as a whole, when it is isolated, has some properties. Another source of difficulties derives from the symmetry requests that the theory imposes in the case of systems containing identical constituents. We discuss these points in detail and we outline recent proposals yielding a consistent solution to the problems arising from the entanglement between a microsystem and a macrosystem which unavoidably occurs in a measurement process. In particular we take into account the so called “collapse” theories which embody a mechanism forbidding, at an appropriate level, the persistence of superpositions and, as a consequence, lead, in general, to the emergence of precise individual properties for macroscopic systems. We then pass to a critical analysis of the difficulties related to the identity of the constituents. We stress that various misunderstandings characterize the treatment of this problem and we make fully clear how one has to deal with the very concept of entangled systems when identical constituents are involved. The ensuing picture should make clear to which extent one can still consistently ground the distinction between the parts and the whole in a genuinely quantum context. (shrink)